Midnight at the start of the first day of the current month is given by:
// first midnight in this month
DateMidnight first = new DateMidnight().withDayOfMonth(1);
// last midnight in this month
DateMidnight last = first.plusMonths(1).minusDays(1);
If starting from a java.util.Date, a different DateMidnight constructor is used:
// first midnight in java.util.Date's month
DateMidnight first = new DateMidnight( date ).withDayOfMonth(1);
Joda Time java doc – https://www.joda.org/joda-time/apidocs/overview-summary.html